Evolution of Thin-Film Wrinkle Patterns on a Soft Substrate: Direct Simulations and the Effects of the Deformation History.

Surface wrinkling instability in thin films attached to a compliant substrate is a well-recognized form of deformation under mechanical loading. The influence of the loading history on the formation of instability patterns has not been studied. In this work, the effects of the deformation history involving different loading sequences were investigated via comprehensive large-scale finite element simulations. We employed a recently developed embedded imperfection technique which is capable of direct numerical predictions of the surface instability patterns and eliminates the need for re-defining the imperfection after each analysis step. Attention was devoted to both uniaxial compression and biaxial compression. We show that, after the formation of wrinkles, the surface patterns could still be eliminated upon complete unloading of the elastic film-substrate structure. The loading path, however, played an important role in the temporal development of wrinkle configurations. With the same final biaxial state, different deformation histories could lead to different surface patterns. The finding brings about possibilities for creating variants of wrinkle morphologies controlled by the actual deformation path. This study also offers a mechanistic rationale for prior experimental observations.

Direct numerical simulations of three-dimensional surface instability patterns in thin film-compliant substrate structures.

A comprehensive numerical study of three-dimensional surface instability patterns is presented. The formation of wrinkles is a consequence of deformation instability when a thin film, bonded to a compliant substrate, is subject to in-plane compressive loading. We apply a recently developed computational approach to directly simulate complex surface wrinkling from pre-instability to post-instability in a straightforward manner, covering the entire biaxial loading spectrum from pure uniaxial to pure equi-biaxial compression. The simulations use embedded imperfections with perturbed material properties at the film-substrate interface. This approach not only triggers the first bifurcation mode but also activates subsequent post-buckling states, thus capable of predicting the temporal evolution of wrinkle patterns in one simulation run. The state of biaxiality is found to influence the surface pattern significantly, and each bifurcation mode can be traced back to certain abrupt changes in the overall load-displacement response. Our systematic study reveals how the loading condition dictates the formation of various instability modes including one-dimensional (1D) sinusoidal wrinkles, herringbone, labyrinth, and checkerboard.

Instabilities of Thin Films on a Compliant Substrate: Direct Numerical Simulations from Surface Wrinkling to Global Buckling.

For structures consisting of a thin film bonded to a compliant substrate, wrinkling of the thin film is commonly observed as a result of mechanical instability. Although this surface undulation may be an undesirable feature, the development of new functional devices has begun to take advantage of wrinkled surfaces. The wrinkled structure also serves to improve mechanical resilience of flexible devices by suppressing crack formation upon stretching and bending. If the substrate has a reduced thickness, buckling of the entire structure may also occur. It is important to develop numerical design tools for predicting both wrinkle and buckle formations. In this paper we report a comprehensive finite element-based study utilizing embedded imperfections to directly simulate instabilities. The technique overcomes current computational challenges. The temporal evolution of the wrinkling features including wavelength and amplitude, as well as the critical strains to trigger the surface undulation and overall structural buckling, can all be predicted in a straightforward manner. The effects of model dimensions, substrate thickness, boundary condition, and composite film layers are systematically analyzed. In addition to the separate wrinkling and buckling instabilities developed under their respective geometric conditions, we illustrate that concurrent wrinkling and buckling can actually occur and be directly simulated. The correlation between specimen geometry and instability modes, as well as how the deformation increment size can influence the simulation result, are also discussed.